Eda Finals Flashcards
Finite – countable
DISCRETE PROBABILITY DISTRIBUTION
a random variable that has countable values, such as a list of non-negative integers.
discrete random variable
a term used to describe any process by which several chance observations are generated.
Statistical Experiment
a function whose value is a real number determined by each element in the sample space.
Random Variable
a sample space containing a finite number of possibilities or an unending sequence with as many elements as there are whole numbers.
Discrete Sample Space
a random variable whose set of possible outcomes is countable.
Discrete Random Variable
a sample space containing an infinite number of possibilities equal to the number of points on a line segment.
Continuous Sample Space
can take on values on a continuous scale.
Continuous Random Variable
TYPES OF DISCRETE PROBABILITY DISTRIBUTION
1.Binomial Probability Distribution
2.Poisson Distribution
3.Bernoulli Distributions
is a probability experiment that satisfies the following four requirements.
BINOMIAL PROBABILITY DISTRIBUTION
is a kind of discrete probability distribution that is useful when the mean, μ, of the distribution is large and the probability of success, p, is small when the independent variables occur over a period of time.
POISSON’S DISTRIBUTION
⮚Infinite – not countable
⮚no negative integer
CONTINUOUS PROBABILITY DISTRIBUTION
TYPES OF CONTINUOUS PROBABILITY
1.Normal Distribution
2.Exponential Distribution
➢the most important continuous probability distribution in the entire field of statistics.
➢Its graph, called the ‘‘normal curve’’, is the bell-shaped curve, which approximately describes many phenomena that occur in nature, industry and research.
NORMAL DISTRIBUTION
A continuous random variable X having the bell-shaped distribution
normal random variable.
➢A statistical distribution that models the time between events
EXPONENTIAL DISTRIBUTION
➢if X and Y are two random variables, the probability distribution that defines their simultaneous behaviour
JOINT PROBABILITY DISTRIBUTION
➢If X and Y are two discrete random variables, the probability distribution for their simultaneous occurrence can be represented by a function with values f(x, y) for any pair of values (x, y) within the range of the random variables X and Y. It is customary to refer to this function as the joint probability distribution of X and Y.
DISCRETE RANDOM VARIABLE
➢The function f ( x, y) is a joint probability distribution or probability mass function of the discrete random variables X and Y if
DISCRETE CASE
➢The case where both variables are continuous is obtained easily by analogy with discrete case on replacing sums by integrals. Thus, the joint probability function for the random variables X and Y (or, as it is more commonly called, the joint density function of X and Y). The function f(x, y) is a joint density function of the continuous random variables X and Y if
CONTINUOUS CASE
used to make decisions and draw conclusions about populations. These techniques utilize the information in a sample for a drawing conclusions.
Statistical Inference
Statistical inference has one major areas which is the parameter estimation. In practice, the engineer will use sample data to compute a number that is in some sense a reasonable value (a good guess) of the true population mean. This number is called ………
➢point estimate.
➢process of using the data available to estimate the unknown value of a parameter when some representative statistical model has been proposed for the variation observed in some chance phenomenon.
POINT ESTIMATION
A point estimate of some population parameter θ is a single numerical value of a statistic. The statistic is called the……..
point estimator.
